U.S. Secretary of State Mike Pompeo and Russian Foreign Minister Sergei Lavrov have said many differences remain between Washington and Moscow, but that talks they held today in the Russian Black Sea resort of Sochi are a step toward improving bilateral relations.

Pompeo and Lavrov, speaking at a joint news conference after the talks on May 14, said they discussed a wide range of issues, including nuclear disarmament, the atomic accord with Iran and Tehran's regional actions, the situation in Venezuela, and other international issues.

'We fundamentally do not see a war with Iran,' Pompeo said, referring to the current tensions between Tehran and Washington.

The talks came ahead of a planned meeting between Pompeo and Russian President Vladimir Putin later in the day -- the highest-level formal discussions between U.S. and Russian officials since July 2018, when U.S. President Donald Trump and Putin met in Finland.

Lavrov said he had 'frank and useful' discussions with Pompeo on a wide array of issues, including Iran, Venezuela, and Syria.

'We discussed in detail the situation regarding bilateral affairs and exchanged opinions on Venezuela, Syria, and the state of affairs regarding the Joint Comprehensive Plan of Action for Iran,' Lavrov said, using the official name for the landmark 2015 nuclear agreement between Iran and world powers.

Pompeo said he urged Russia to end its support for Venezuelan President Nicolas Maduro, but his call was flatly rejected by Moscow.

'The time has come for Nicolas Maduro to go. He has brought nothing but misery to the Venezuelan people, and we hope that Russian support for Maduro will end,' Pompeo told the news conference.

He also said they discussed Russia's interference in the United States' domestic affairs.

Earlier, Pompeo told Lavrov that President Donald Trump is 'committed' to improving relations with Russia.

At the start of his meeting with Lavrov, Pompeo said Russia and the United States might not agree on everything, but there was room for cooperation -- particularly on counterterrorism and nuclear nonproliferation.

Lavrov expressed hope that the sides 'will be able to hammer out specific proposals aimed at steering Russian-American relations out of the current sad state.'

Lavrov said it was 'time to start building a new, more responsible and constructive model of mutual perception of each other,' adding, 'We are ready for this.'

'This mistrust that we have hinders both your security and ours,' Lavrov said.

Earlier in the day, Pompeo tweeted that his talks with Putin and Lavrov 'will highlight a number of important topics.'

'On some issues we may agree, on others we may disagree, but when its in our national interests, it is our responsibility to find a way forward,' Pompeo's tweet said.

Setting up a new meeting between Trump and Putin could also be on Pompeo's agenda, after the U.S. president on May 13 said he would hold talks with Putin during the upcoming Group of 20 summit to be held in Japan in June.

However, Kremlin spokesman Dmitry Peskov was quoted by Russian news agencies as saying that Washington had not requested a meeting between Trump and Putin.

'There have been no requests. But there have been no agreements yet as well,' Peskov said.

Ahead of the talks with Pompeo, Putin toured a military flight test center in southern Russia and inspected a new nuclear-capable 'hypersonic' missile dubbed Kinzhal (Dagger).

Peskov rejected allegations that the apparent show of force was designed to send a message to the United States, saying, 'There's no need to come up with any conspiracy theories here.'

The State Department has said that the agenda of Pompeo's meetings in Sochi would include arms control, the crisis in Venezuela, and the conflicts in Ukraine and Syria, as well as Iran.

'Modern Reality'

All of those issues are areas where the United States and Russia are at direct odds with one another.

'The starting point we have to have when we discuss our policy toward Russia...is to acknowledge frankly that Russia has taken a series of aggressive and destabilizing actions on the global stage,' a senior State Department official told reporters on May 10.

The official, who spoke on condition of anonymity, added that Pompeo's trip was 'an opportunity to make those points clear to the Russian government and what our expectations are and [to] see how to forge a path forward.'

Arms control will be high on the agenda of the talks, in particular an 'arms-control agreement that reflects modern reality,' according to the official.

In February, the United States suspended participation in the 1987 Intermediate-Range Nuclear Forces (INF) Treaty because of what it says is Russia's development and deployment of a missile system that violates the pact.

Moscow, which denies the accusation, later followed suit.

'One-Sided' Deal

The INF Treaty banned the United States and Russia from developing, producing, and deploying ground-launched cruise or ballistic missiles with ranges between 500 and 5,500 kilometers.

Moscow and Washington have also been gearing up for talks on how and whether to extend the New START treaty, the only U.S.-Russia arms control pact limiting deployed strategic nuclear weapons.

It is set to expire in February 2021 but can be extended for five years if both sides agree.

Trump has called the New START treaty concluded in 2010 by his predecessor, Barack Obama, a 'bad deal' and 'one-sided.'

Trump spoke with Putin by phone last week and said they discussed the possibility of a new accord limiting nuclear arms that could eventually include China.

But Chinese Foreign Minister Wang Yi, who met with Lavrov in Sochi on May 13, said his country wasn't interested in negotiating a nuclear arms control treaty with the United States and Russia.

Wang told reporters after the meeting that China 'has no interest' in being part of such a treaty.

He said China keeps its arsenal of nuclear weapons at 'the minimal level to ensure the defense policies.'

'Talks Instead Of Threats'

Pompeo had originally been due to travel to Moscow on May 13 but canceled that visit to instead discuss Iran with EU and NATO officials in Brussels.

Pompeo shared information on 'escalating' threats from Tehran, according to Brian Hook, the U.S. special representative for Iran.

'The secretary wanted to share some details behind what we have been saying publicly,' Hook said. 'We believe that Iran should try talks instead of threats. They have chosen poorly by focusing on threats.'

Hook said Pompeo, while in Brussels, also discussed reported attacks on several oil tankers off the coast of the United Arab Emirates.

Hook declined to comment on whether he believed there was the possibility of an Iranian role.

The U.A.E. said on May 12 that four commercial vessels were sabotaged near Fujairah emirate.

Saudi Arabia said on May 13 that two of its oil tankers were among those attacked.